### Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

### Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

### Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

# Coloured Edges

##### Age 11 to 14 Challenge Level:

 There is a set of tiles which are all different and coloured just on the edges. Each edge on a tile is a different colour. For example: Altogether $10$ different colours are used for the edges, and there is an equal number of edges of each colour used throughout the set. The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?